Michele Bachman was expected to be facing a hard fight, even though boundary changes this year favoured her. Photograph: Chris O'Meara/AP

The Tea Party darling and failed contender for the Republican nomination Michele Bachmann has said she is "humbled" to have been re-elected to Congress as projections showed her on course to narrowly defeat her Democratic challenger in Minnesota after a very expensive campaign.

Bachmann, who pulled out of the race to become nominee in January after only 5% of Republicans in Iowa entrusted her with their vote, led the businessman Jim Graves by 3,256 votes, with 98.2% of precincts reporting, according to unofficial state elections returns.

Both CNN and the Associated Press called the contest for the incumbent, who will return to Congress for a fourth term.

In a statement, the 56-year-old said: "It has truly been an honour and a privilege to represent the people of Minnesota's sixth district in Congress, and I am humbled that they have placed their trust in me for another term."

A conservative firebrand and evangelical Christian who played a big part in the growth of the Tea Party movement, Bachmann was running in the sixth congressional district in Minnesota, which after boundary changes earlier this year became even more Republican than it had been. However, she has never won more than 53% in the district, and this victory looked likely to be even tighter than in previous years.

According to figures from the Centre for Responsive Politics, as of October the battle between Bachmann and Graves was the most expensive House race in the country, with the candidates spending $20.8m (£13m) and raising $22.7m. The Republican outspent Graves by more than 12 to one, the centre said.

During her campaign, Bachmann sought to denounce her opponent, a successful businessman who founded the AmericInn hotel chain and now heads Graves Hospitality, as a supporter of Barack Obama's health insurance programme; he accused her of being an ineffective congresswoman.

Bachmann's nomination bid thrust her into the national spotlight but her critics said it had lessened her ability to focus on her district. It also revealed her propensity for making gaffes and outlandish accusations, such as her claim that the Muslim Brotherhood had "deep penetration" within government.

In her statement, Bachmann said: "I am extremely grateful to my dedicated volunteers for spending countless hours knocking on doors and making phone calls. I pledge to continue to work every day to create jobs and do everything I can to make life more affordable for Minnesota's families. Our children and grandchildren deserve a future filled with opportunity in a country that is safe and secure, and that's what I'm fighting for in Washington."